1. Field of the Invention
The present invention relates to an apparatus for simulating complex systems at a high rate of speed and also to a method of modulating signals for encryption.
2. Description of the Related Art
Numerical models for describing quantitative changes are a type of arbitrary function generator that produces specific functions based on the parameters provided. The models can be simulated at high speeds with an analog arithmetic circuit and, in fact, were simulated with analog computers in the past. However, these analog arithmetic circuits are rarely used anymore because the circuits have to be rewired for each problem and enormous circuits are required when the problems are of a large scale. Subsequently, wire connections in the analog arithmetic circuits were modified electrically through software, but this analog calculation method is no longer used because integrating complex circuits is extremely difficult.
In order to simulate a phenomenon having multiple variables at a high rate of speed, it is advantageous to generate arbitrary functions with an analog arithmetic circuit. For this method to be practical, however, it is necessary to programmably generate functions of different types without needing to physically change the wiring of the arithmetic circuit. Further, the circuit must have a simple construction such as RAM that facilitates high integration by repeating simple mask patterns. It is also necessary to minimize the number of components needed to construct the circuit.
A generalized Lotka-Volterra equation can be used in plant growth models or for the dynamics of biological communities and is represented by a differential equation such as the following.                                           ⅆ                          x              i                                            ⅆ            t                          =                                            x              i                        ⁡                          (                                                r                  i                                +                                                      ∑                                          j                      =                      1                                        m                                    ⁢                                                            μ                      ij                                        ⁢                                          x                      j                                                                                  )                                ⁢                                           ⁢                      (                                          i                =                1                            ,              2              ,              …              ⁢                                                           ,              n                        )                                              Equation 1            
Here, xi is the size of a population i representing the elements of a system; μij is a constant of interaction between the elements; and ri is an inherent constant for each element representing the growth rate of the population i. When n is sufficiently large, this equation can approximate a positive arbitrary continuous function of an arbitrary precision by varying n and μij, it is possible to generate patterns of xi that change in various ways. Accordingly, in addition to modeling phenomena, this calculation has a wide range of applications as an arbitrary waveform generator. The present invention focuses on the symmetry of this equation to perform high-speed emulation by performing the calculation in hardware or using parallel processing with multiple digital computers.